A316604 Replacing each digit d in decimal expansion of n with d^2 yields a new prime when done recursively three times.

11, 101, 131, 133, 1013, 2111, 2619, 3173, 3301, 4111, 5907, 8463, 9101, 10033, 10111, 12881, 13833, 14021, 14821, 15443, 16771, 17501, 17831, 18621, 21519, 21567, 28609, 29309, 31133, 31233, 33131, 41621, 42621, 44181, 44421, 44669, 45921, 52707, 55847, 59023

Offset: 1

Author

K. D. Bajpai, Jul 08 2018

Keywords

• nonn
• base

Examples

			2619 is a term because replacing each digit d by d^2, recursively three times, a prime number is obtained: 2619 -> 436181 (prime); 436181 -> 169361641 (prime); 169361641 -> 13681936136161 (prime).
3173 is a term because replacing each digit d by d^2, recursively three times, a prime number is obtained: 3173 -> 91499 (prime); 91499 -> 811168181 (prime); 811168181 -> 6411136641641 (prime).
		

Crossrefs

Cf. A048385, A048388, A048390, A048393.

Programs

Mathematica

A316604 = {}; Do[ a=FromDigits[Flatten[IntegerDigits /@ (IntegerDigits[n]^2)]]; b=FromDigits[Flatten[IntegerDigits /@ (IntegerDigits[a]^2)]]; c=FromDigits[Flatten[IntegerDigits /@ (IntegerDigits[b]^2)]]; If[PrimeQ[a] && PrimeQ[b] && PrimeQ[c], AppendTo[A316604,n]], {n,100000}]; A316604

PARI

replace_digits(n) = my(d=digits(n), s=""); for(k=1, #d, s=concat(s, d[k]^2)); eval(s)
is(n) = my(x=n, i=0); while(1, x=replace_digits(x); if(!ispseudoprime(x), return(0), i++); if(i==3, return(1))) \\ Felix Fröhlich, Jul 08 2018